University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below112192810.22098/jfga.2022.11723.1072ENXinyue ChengSchool of Mathematical Sciences,
Chongqing Normal University,
Chongqing, ChinaHong ChengSchool of Mathematical Sciences,
Chongqing Normal University,
Chongqing, ChinaXibin ZhangSchool of Mathematical Sciences,
Chongqing Normal University,
Chongqing, ChinaJournal Article20221031This paper mainly studies the volume comparison in Finsler geometry under the condition that the weighted Ricci curvature Ric<sub>∞</sub> has a lower bound. By using the Laplacian comparison theorems of distance function, we characterize the growth ratio of the volume coefficients. Further, some volume comparison theorems of Bishop-Gromov type are obtained.https://jfga.uma.ac.ir/article_1928_f6c6d304b2cd56d0c1224267b439d5ae.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201Some results in generalized symmetric square-root spaces1319192910.22098/jfga.2022.11879.1075ENMilad Zeinali LakiDepartment of Mathematics, University of Mohaghegh Ardabili, p.o.box. 5619911367, Ardabil-Iran.0000-0003-2984-4605Journal Article20221203In this paper, we study generalized symmetric Finsler spaces with special (α , β ) -space. In fact, we study this spaces with square-root metric and we prove that generalized symmetric (α , β ) -spaces with square-root metric must be Riemannian.https://jfga.uma.ac.ir/article_1929_f1d3158fe0cc20282894d381fd0e3bdf.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On 3-Dimensional Finsler Manifolds2028193010.22098/jfga.2022.11803.1073ENMohammad ShahbaziNiaFaculty of Science, Department of Mathematics
University of Qom,
Qom. IranJournal Article20221114Every Landsberg metric and every Landsbeg metric is a weakly Landsberg metric, but the converse is not true generally. Let (M, F) be a 3-dimensional Finsler manifold. In this paper, we find a condition under which the notions of weakly Landsberg metric and Landsberg metric are equivalent.https://jfga.uma.ac.ir/article_1930_7ce56e5f6ef396532e8761e2cc4e43a2.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On Conformally Flat 5-th root (α, β)-Metrics with Relatively Isotropic Mean Landsberg Curvature2940193210.22098/jfga.2022.11477.1070ENMarzeiya AminiDepartment of Mathematics, Faculty of science University of Qom, Qom, Iran.Journal Article20220908In this paper, we study conformally ﬂat 5-th root (α, β)-metrics. We prove that every<br />conformally ﬂat 5-th root (α, β)-metric with relatively isotropic mean Landsberg curvature<br />must be either Riemannian metrics or locally Minkowski metrics.https://jfga.uma.ac.ir/article_1932_034972aeacb76b02846211fa6f27ae9c.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201Reversibility and Sub-reversibility of Finsler Metrics4149193310.22098/jfga.2022.11468.1069ENHassan SadeghiDepartment of Mathematics, Faculty of Science, University of Qom
Qom. IranJournal Article20220907In order to extend the sphere theorem for Finsler metrics, the concept of reversibil-<br />ity introduced by H-B. Rademacher for a compact Finsler manifold. In this paper, we<br />extend this notion to the general Finsler manifolds. Then we find an upper bound for<br />the reversibility of some important spherically symmetric Finsler metrics. Furthermore,<br />we introduce the concept of sub-reversibility for a general Finsler manifold and obtain a<br />non-zero lower bound for this new quantity.https://jfga.uma.ac.ir/article_1933_791cdd7e7e033796feea46857f594c16.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On the Flag Curvature of Invariant Square Metrics5056193410.22098/jfga.2022.11680.1071ENParastoo HabibiDepartment of Mathematics, Islamic Azad University, Astara branch, Astara, IranJournal Article20221016In this paper, we give an explicit formula for the flag curvature of invariant square metric and Randers change of square metric.https://jfga.uma.ac.ir/article_1934_62d93df184365ecb119babbc39b3f172.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On Square-type Finsler Metrics of Vanishing Flag Curvature5763193910.22098/jfga.2022.11459.1068ENTahere RajabiDepartment of Mathematics, Faculty of Science, University of Qom
Qom. IranJournal Article20220907In this paper, we construct a family of Finsler metrics, called square-type Finsler metrics. We obtain the flag curvature of this metric. Then we find a necessary and sufficient condition under which the flag curvature of square-type Finsler metrics becomes zero.https://jfga.uma.ac.ir/article_1939_a17cb91802a8b71038d132f140ceae4e.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On Projectively Related (α,β)-Metrics6477194010.22098/jfga.2022.11915.1078ENFarzaneh KamelaeiDepartment of Mathematics, Karaj Branch, Islamic Azad University
Karaj, IranJournal Article20221212In this paper, we find necessary and sufficient conditions under<br />which the infinite series metric and Randers metric on a manifold M of dimen<br />sion n >3 be projectively related.https://jfga.uma.ac.ir/article_1940_2bc05cb94a13e6041fe19b3e07e80b1c.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201General (α, β)-Metrics With Constant Ricci and Flag Curvature7890194310.22098/jfga.2022.11876.1074ENSEMAIL ULGENDepartment of Industrial Engineering, Antalya Bilim University
Ciplakl Mahallesi Farabi Caddesi No: 23, Dösemealt, Antalya, 07190, Turkey0000-0003-1381-1577Journal Article20221201General (α, β) metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a general (α, β) metrics. In this paper, we study the general (α, β) metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover we study the vanishing non-Riemannian quantity χ-curvature.https://jfga.uma.ac.ir/article_1943_1936679dff9f5497c824c173704bdcdc.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On Einstein Finsler warped product metrics9198194810.22098/jfga.2022.11907.1076ENMehran GabraniDepartment of Mathematics, Faculty of Science,
Urmia University, Urmia, Iran.Bahman RezaeiaDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.Esra Sengelen SevimDepartment of Mathematics, Istanbul Bilgi University, 34060, Eski
Silahtaraga Elektrik Santrali, Kazim Karabekir Cad. No: 2/13 Eyupsultan,
Istanbul, Turkey.Journal Article20221208In this paper, we study the Finsler warped product metric which is Einstein. We find equation that characterize Einstein Finsler warped product metrics with vanishing Douglas curvature. Moreover, we obtain the differential equation that characterizes Einstein Finsler warped product metrics of locally projectively flat.https://jfga.uma.ac.ir/article_1948_194f14aba749a963bdcd184a060a038e.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201On the spectral geometry of 4-dimensional Lorentzian Lie group99118195910.22098/jfga.2022.11917.1080ENDavood SeifipourDepartment of Mathematics, Abadan Branch, Islamic Azad University,
Abadan, IranJournal Article20221212The main focus of this paper is concern to the study on the point-wise Osserman structure on 4-dimensional Lorentzian Lie group. In this paper we study on the spectrum of the Jacobi operator and spectrum of the skew-symmetric curvature operator on the non-abelian 4-dimensional Lie group G, whenever G equipped with an orthonormal left invariant pseudo-Riemannian metric g of signature (-;+;+; +), i.e, Lorentzian metric, where e1 is a unit time-like vector. The Lie algebra structure in dimension four has key role in our investigation, also in this case we study on the classification of 1-Stein and mixed IP spaces. At the end we show that G does not admit any space form and Einstein structures.https://jfga.uma.ac.ir/article_1959_92e7e83227cf41270eda835cd043db35.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003220221201Para-Kähler hom-Lie algebras of dimension 2119138196010.22098/jfga.2022.11916.1079ENEsmaeil PeyghanDepartment of Mathematics, Faculty of Science, Arak university, Arak, IranLeila NourmohammadifarDepartment of Mathematics, Faculty of Science, Arak University
Arak, 38156-8-8349, Iran.Journal Article20221212In [12], authors introduced some geometric concepts such as (almost) product, para-complex, para-Hermitian and para-Kähler structures for hom-Lie algebras and they presented an example of a 4-dimensional hom-Lie algebra, which contains these concepts. In this paper, we classify two-dimensional hom-Lie algebras containing these structures. In particular, we show that there doesn't exist para-Kahler proper hom-Lie algebra of dimension 2.https://jfga.uma.ac.ir/article_1960_c36f1d44ba66eb9cdf7397e967864f41.pdf